arXiv subjects

Jean-Christophe Pain

Publications and source records attributed to Jean-Christophe Pain.

148 records · Page 9Linked to original sources

arXiv2009

Jensen-Feynman approach to the statistics of interacting electrons

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists in a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.

physics.atom-ph↗

arXiv2009

Effect of third- and fourth-order moments on the modeling of Unresolved Transition Arrays

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p-3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach ...).

physics.atom-ph↗

arXiv2007

A model of dense-plasma atomic structure for equation-of-state calculations

A model of dense plasmas relying on the superconfiguration approximation is presented. In each superconfiguration the nucleus is totally screened by the electrons in a Wigner-Seitz sphere (ion-sphere model). Superconfigurations of the same charge are grouped into ions. It is shown that boundary values of the wavefunctions play a crucial role in the form of the Virial theorem from which the pressure formula is derived. Finally, a condition is presented and discussed, which makes the ion-sphere model variational when bound electrons are treated quantum-mechanically and free electrons quasi-classically.

physics.atom-ph↗

arXiv2007

Quantum-statistical equation-of-state models of dense plasmas: high-pressure Hugoniot shock adiabats

We present a detailed comparison of two self-consistent equation-of-state models which differ from their electronic contribution: the atom in a spherical cell and the atom in a jellium of charges. It is shown that both models are well suited for the calculation of Hugoniot shock adiabats in the high pressure range (1 Mbar-10 Gbar), and that the atom-in-a-jellium model provides a better treatment of pressure ionization. Comparisons with experimental data are also presented. Shell effects on shock adiabats are reviewed in the light of these models. They lead to additional features not only in the variations of pressure versus density, but also in the variations of shock velocity versus particle velocity. Moreover, such effects are found to be responsible for enhancement of the electronic specific heat.

physics.plasm-ph↗